Fundamentals of Math - old

Fundamentals of Mathematics

Unlike multiplication/division where you could simplify any combination of numerator and denominator before performing the operation addition/subtraction does not allow uncoordinated pairs.

Okay to Simplify

Not Okay to Simplify

3 6 1 5 It is okay to simplify 3 6 before you add. +

7 11 2 8 It is okay to simplify 2 8 before you subtract. −

3 5 2 3 You cannot divide each three by 3. +

13 16 4 7 You cannot divide four and sixteen by 4. −

_________________________________________________________________________________________ Warning: With adding and subtracting it’s also not always

advisable to simplify the fractions up front. Since addition/subtraction requires like denominators, you run the risk of losing that aspect between the two fractions by simplifying from the start. _________________________________________________________________________________________ To add/subtract fractions with unlike denominators you must first create equivalent fractions (see Equivalent Fractions ). 1. Find a multiple of the two denominator integers. 2. Ask yourself what would I have to multiply denominator 1 by to equal the multiple I identified in step 1? 3. Multiply numerator and denominator 1 by the multiplier found in step 2. 4. Repeat steps 2 and 3 but with your second fraction.

Example 2.2.6

2 3

7 10

+

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, … 10: 10, 20, 30, … “30” is the LCM

Step 1: Find the LCM between 3 and 10.

3 × ? = 30

Re-write the first fraction as an equivalent fraction, so the denominator changes to the LCM. Re-write the second fraction as an equivalent fraction, so the denominator changes to the LCM.

The answer is 10.

Step 2:

2 × 10 3 × 10

20 30

=

10 × ? = 30

The answer is 3.

Step 3:

7 × 3 10 × 3

21 30

=

Add the fractions and simplify if possible.

2 3

7 10

20 30

21 30

20 + 21 30

41 30

Step 4:

+

⟹

+

=

=

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